Find the parametric and symmetric forms of the equation of t

Find the parametric and symmetric forms of the equation of the line that passes through the points P (1, 4, 5) and Q (3, -2, 1).

Solution

Vector passing these two points is <3-1,-2-4,1-5>= <2,-6,-4>

We can use any of the point to find the parametric equation.Lets use point P

x=1+2t   , y=4-6t    ,z=5-4t

Solving for t gives the symmetric equation

(x-1)/2= (y-4)/-6   =   (z-5)/-4